Problem: The value of $\sqrt{45}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Consider the perfect squares near $45$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $36$ is the nearest perfect square less than $45$ $49$ is the nearest perfect square more than $45$ So, we know $36 < 45 < 49$ So, $\sqrt{36} < \sqrt{45} < \sqrt{49}$ So $\sqrt{45}$ is between $6$ and $7$.